this paper we introduce a new scenario for the Parrondo's paradox which involves a set of players ~ [7] and where one of the games has been replaced by a redistribution of the capital owned by the players. It will be shown that even though each individual player (when playing alone) has a negative winning expectancy, the redistribution of money brings each player a positive expected gain. This result holds even in the case that the redistribution of capital is directed from the richer to the poorer, although in this case the distribution of money amongst the players is more uniform and the total gain is less

Abstract not found

Game theory is a well established field with applications in many areas including the social sciences, biology, and computer science [6]. Recently, however, researchers in quantum computation have begun to study the implications of games set in the quantum domain (i.e. game theoretical situations where either one or more players have quantum computational power or where the implementation of strategies uses some form of quantum information). Such a setting allows for entanglement and superpositions of strategies and evaluation of payoffs using quantum measurement. This approach to game theory, according to some scholars in the field, could help us understand certain physical systems, improve economic markets, and develop quantum algorithms. I have conducted an investigation into quantum game theory. I have constructed simulation tools using Maple that, along with research into related work, have helped gain some insight into this new field. The important solutions in classical game theory are usually Nash equilibria. What do they look like in the quantum realm? In what

For my project I simulated a quantum random walk in one plus one dimensions with a ratcheting potential applied. The particle begins at the origin and after running the simulation for one hundred time steps the most probable final position was calculated and then graphed according to its initial condition. These results were analyzed to determine the dependence on initial condition of final position.

We propose a quantum implementation of a capital-dependent Parrondo’s paradox that uses O(log2 (n)) qubits, where n is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show simulation results.

Limit theorems and absorption problems for one-dimensional correlated random walks

Limit theorems and absorption problems for one-dimensional correlated random walks